Quantum algorithms for discrete spacetimes

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There are various indications that spacetime, fundamentally or effectively, may be discrete. These include the finiteness of black hole entropy, the discrete spectrum of the volume operator in loop quantum gravity and dualities in string theory. To capture the phenomenology of such a discrete substratum, how continuity emerges in larger scales, and where to look for predictions and new physics one needs to numerically simulate the physics on these discrete structures, especially since the randomness imposed by Lorentz invariance prohibits certain analytic approaches1. One of the greatest challenges, however, is that interesting phenomena arise in larger scales than those that are computationally tractable with classical computing. On the other hand, the mathematical formulation of spacetime as a discrete, random, partial order2, give grounds to believe that quantum algorithms could offer advantages. Specifically, there are already many quantum algorithms for graph problems offering advantage. Modifying such algorithms to deal with discrete orders is natural and at the same time novel and challenging, because of the large valence (number of nearest neighbours of an element) of the random orders that model spacetime. Moreover, the physics we will put on the computer is already discrete. Since one of the major obstacles in using quantum algorithms for physics or chemistry, is loss of accuracy and implementation cost of encoding continuous variables in the discrete variables/qubits that quantum computers use, the prospect of useful quantum advantage in a scenario where no approximation is needed is more likely.